An Evolutionary Model for the Stable Marriage Problem

Date of Award

2009

Document Type

Thesis

Degree Name

Bachelors

Department

Natural Sciences

First Advisor

Mullins, David

Keywords

Interdependent Utility, Interdependent Preferences, Stable Matching, Stable Marriage, Evolutionary Economics, Behavioral Economics

Area of Concentration

Mathematics

Abstract

Many variants of the Stable Marriage Problem (a one-to-one matching problem with no bearing on actual marriage) have been explored in the 46 years since the problem was first introduced. We believe our model is the first to be based on the assumption that individuals gain utility both from their own and from their partners' happiness. Participants' initial preferences are formulated the same way as in the original model. In our model, however, participants then reorder their preferences, preferring those pairings which provide the greatest total utility. All preferences are re-ordered until they cease to change (become stable). The participants are then matched via the Gale-Shapley algorithm (in accordance with these new preferences). Our most important discovery is that all (initial) sets of preferences eventually stabilize. We explore, experimentally, the relationship between group size (cardinality of each set) and how many times preferences must be reordered before stabilizing. We explain why and where our model may be applicable and use our model to help explain the disparity in age of first marriage in metropolitan versus nonmetropolitan areas. Finally, we discuss conjectures and variations for possible future study.

Rights

This bibliographic record is available under the Creative Commons CC0 public domain dedication. The New College of Florida, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.

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